15th Probability Day Erlangen-München

The probability day takes place on Friday, June 17, 2016, in room B005 at the mathematical institute of the Ludwig-Maximilian-Universität München. Information how to get to the mathematical institute can be found here. It takes approximately 25 minutes to walk from the train station to the mathematical institute.

Speakers

Jean Bertoin (Zürich): Local explosion in growth-fragmentation processes (based on a joint work with Robin Stephenson)Abstract: Growth-fragmentation processes describe a family of particles which can grow larger or smaller with time, and occasionally split in a conservative manner. In the self-similar case, it is known that a simple Malthusian condition ensures that the process does not locally explode, in the sense that for all times, the masses of all the particles can be listed in non-increasing order. We shall present here the converse: when this Malthusian condition is not verified, then the growth-fragmentation process explodes almost surely. Our proof involves using the additive martingale to bias the probability measure and obtain a spine decomposition of the process, as well as properties of self-similar Markov processes.

Margherita Disertori (Bonn) Nematic phase in a system of long hard rodsAbstract: We consider a two-dimensional lattice model for liquid crystals consisting of long rods interacting via purely hard core interactions, with two allowed orientations defined by the underlying lattice. For this model, we rigorously prove the existence of a nematic phase, i.e., we show that at intermediate densities the system exhibits orientational order, either horizontal or vertical, but no positional order. This is joint work with A. Giuliani.

Alexander Drewitz (Köln) The maximum particle of branching random walk in spatially random branching environmentAbstract: Branching Brownian motion and branching random walk have been the subject of intensive research during the last decades. We consider branching random walk and investigate the effect of introducing a spatially random branching environment; in this context, we are primarily interested in the positions of (the median of) the maximum particle and the so-called ‘breakpoint'. On an analytic level this corresponds to investigating the fronts of the solutions to a randomized Fisher-KPP equation and to the parabolic Anderson model, as well as their relative backlog.